A242172 a(n) = 2^n*binomial((n + 1 + (n mod 2))/2, 1/2).
1, 3, 6, 15, 30, 70, 140, 315, 630, 1386, 2772, 6006, 12012, 25740, 51480, 109395, 218790, 461890, 923780, 1939938, 3879876, 8112468, 16224936, 33801950, 67603900, 140408100, 280816200, 581690700, 1163381400, 2404321560, 4808643120, 9917826435, 19835652870
Offset: 0
Keywords
Programs
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Maple
a := n -> 2^n*binomial((n+1+(n mod 2))/2, 1/2); seq(a(n), n=0..29);
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Mathematica
a[n_] := 2^n*Binomial[(n + 1 + Mod[n, 2])/2, 1/2]; Array[a, 33, 0] (* Amiram Eldar, Mar 04 2023 *)
Formula
a(2*n) = A002457(n).
a(2*n+1) = A033876(n).
a(2*n+2)/2 = a(2*n+1).
Conjecture: (n+1)*a(n) -2*a(n-1) +4*(-n-1)*a(n-2)=0. - R. J. Mathar, May 11 2014
a(n) = A100071(n+2)/2. - Michel Marcus, Sep 14 2015
Sum_{n>=0} 1/a(n) = 2*Pi/sqrt(3) - 2. - Amiram Eldar, Mar 04 2023
a(n) = (n+2)*binomial(n+1,ceiling(n/2))/2. - Wesley Ivan Hurt, Nov 23 2023